5 papers · 1 filter
The Wasserstein--Ebin Metric: A Geometric Lift of Unbalanced Optimal Transport to the space of Riemannian metrics
Martin Bauer, Peter W. Michor, François-Xavier Vialard
We introduce dynamic and static formulations that formally extend unbalanced optimal transport from the space of positive densities to the space of Riemannian metrics. The first co…
The Schouten-Nijenhuis bracket in infinite dimensions
Peter W. Michor
The Schouten-Nijenhuis bracket on smooth infinite-dimensional manifolds is developed in two steps: For summable multivector fields whose pointwise dual are all differential for…
Regularity and completeness of half-Lie groups
Martin Bauer, Philipp Harms, Peter W. Michor
Half Lie groups exist only in infinite dimensions: They are smooth manifolds and topological groups such that right translations are smooth, but left translations are merely requir…
Geometry of infinite dimensional Cartan Developments
Johanna Michor, Peter W. Michor
The Cartan development takes a Lie algebra valued 1-form satisfying the Maurer-Cartan equation on a simply connected manifold to a smooth mapping from into the Lie group. I…
Sobolev metrics on spaces of manifold valued curves
Martin Bauer, Cy Maor, Peter W. Michor
We study completeness properties of reparametrization invariant Sobolev metrics of order on the space of manifold valued open and closed immersed curves. In particular, fo…